The Ducks had a 3-on-1 break in the early seconds of overtime, but Troy Terry's pass to Rickard Rakell was broken up, leading to the breakaway goal by Miller that ended a five-game losing streak against the Ducks.
"In this building, I have had like no success," Miller said. "Even as a team, we have struggled here, so it's a hard building to play in and it's a character win."
Miller has nine overtime goals in his NHL career and owns a seven-game point streak (three goals, eight assists), one short of his NHL career high.
The Ducks took a 1-0 lead at 16:26 of the first period. Hampus Lindholm and Nicolas Deslauriers each banked the puck off the boards to get it ahead to Carrick, who skated in and scored from in close.
"It was important for everyone to get into the game early," Carrick said. "Whether it was hitting a guy, or getting hit, or just having a good cycle shift down low."